Characterizing the Carnot cycles at absolute zero: a reply to “Comment on ‘Proof of the Nernst theorem’”

This reply addresses a recent comment concerning the proof of the Nernst theorem. I clarify how a Carnot engine can consistently operate at $$T=0$$ T = 0 through a continuous deformation of a cycle operating at $$T>0$$ T > 0 . By examining the limit where heat exchange with the cold reservoir vanishes, I show that the Nernst theorem ensures that the concept of temperature remains physically consistent at the absolute zero limit.